Nonlocal Separable Elliptic Equations and Applications

Abstract

The regularity properties of nonlo cal elliptic equations are investigated in abstract weighted Lp spaces. Here, we find sufficient conditions that guarantee the separability of the linear problems. We prove that the corresponding nonlo cal elliptic operator is sectorial and is also a negative generator of an analytic semigroup. In application, the maximal regularity properties of the for degenerate abstract equation in LP norms, and infinite systems of degenerate elliptic integro-differential equations with parameters are obtained.